The "Fat Lady" is a story Seymour told both Franny and Zooey when they were younger. Zooey brings it up over the phone to Franny at the very end of the novel. When Zooey was a child celebrity on "It's a Wise Child," he refused to shine his shoes since he thought the people running the show didn't deserve any respect. Seymour told him to shine his shoes for the Fat Lady, and for some reason, says Zooey, it made sense. Franny chimes in that Seymour told her the same thing – to be funny for the Fat Lady – and that it made sense to her, too.
Fortunately, Zooey interprets this cryptic story for us. Take a look:
"I'll tell you a terrible secret – Are you listening to me? There isn't anyone out there who isn't Seymour's Fat Lady. That includes your Professor Tupper, buddy. […] Don't you know that goddam secret yet? And don't you know – listen to me, now – don't you know who that Fat Lady really is? . . . Ah, buddy. Ah, buddy. It's Christ Himself. Christ Himself, buddy." (Zooey.8.77)
This is very similar to Zooey's "chicken soup for the soul" lesson: spirituality is everywhere, even in the people Franny might find pretentious. Zooey's earlier claim that Franny shouldn't make things personal is reinforced here. According to Zooey, she shouldn't hate professor Tuppet, because Christ lives in Professor Tupper just as he lives in everyone. It's fitting that this lesson came from Seymour – it's almost like Franny's oldest and wisest brother is speaking to her through Zooey.